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In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s).

$ f(x) = \frac{1}{4} x^2 - 2x - 12 $

Vertex: $(4,-16)$Axis of symmetry: $x=4$$x$ -intercepts: $(12,0),(-4,0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

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start off here by writing this in the form. And the reason for doing that is that the Vertex will be h k. So here we have one over four ex clear minus a dicks. Parentheses minus twelve. Now we'LL go ahead and complete the square. So half of eight is four square that you get sixteen. But notice we didn't just add in the forth the sixteen here because we have one fourth. So we really added it. Four. So we'll make up for this vice attracting for And then we're still completing the square And there we go We see that the vertex is the point four minus sixteen So for here in the eggs And then I'm going down by twos in the white direction And then next up we have access of symmetry This has always given by x equals age So in our case, that's for So if I come over here to the graph, that would be more or less This photo Klein right here passing through the Vertex So that equation X equals four. And also we have X intercepts do this in blue. So as usual we take our function f so we can use this or we can use this expression over here. Set that equals zero. Push the sixteen to the other side. Multiply that four over. So square that plus or minus eight. So X equals four plus or minus eight. And go ahead and plug in both of those values. The plus in the minus. And that will give you it's fallen minus four. So we know that our graph would pass through this point here. And by the way that I draft this out, we can't see the X equals twelve. But that should also be planet on the graph. And then you would just go ahead and possibly plot in a few more points, for example, f of zero negative twelve. So we have some points here, so and that's a graph.

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